Coherent eddies and turbulence in vegetation canopies: The mixing-layer analogy

This paper argues that the active turbulence and coherent motions near the top of a vegetation canopy are patterned on a plane mixing layer, because of instabilities associated with the characteristic strong inflection in the mean velocity profile. Mixing-layer turbulence, formed around the inflectional mean velocity profile which develops between two coflowing streams of different velocities, differs in several ways from turbulence in a surface layer. Through these differences, the mixing-layer analogy provides an explanation for many of the observed distinctive features of canopy turbulence. These include: (a) ratios between components of the Reynolds stress tensor; (b) the ratio K _H/K _M of the eddy diffusivities for heat and momentum; (c) the relative roles of ejections and sweeps; (d) the behaviour of the turbulent energy balance, particularly the major role of turbulent transport; and (e) the behaviour of the turbulent length scales of the active coherent motions (the dominant eddies responsible for vertical transfer near the top of the canopy). It is predicted that these length scales are controlled by the shear length scale % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitamaaBa% aaleaacaWGtbaabeaakiabg2da9iaadwfacaGGOaGaamiAaiaacMca% caGGVaGabmyvayaafaGaaiikaiaadIgacaGGPaaaaa!3FD0!\[L_S = U(h)/U'(h)\] (where h is canopy height, U(z) is mean velocity as a function of height z, and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyvayaafa% Gaeyypa0JaaeizaiaadwfacaGGVaGaaeizaiaadQhaaaa!3C32!\[U' = {\rm{d}}U/{\rm{d}}z\]). In particular, the streamwise spacing of the dominant canopy eddies is _x = mL _s, with m = 8.1. These predictions are tested against many sets of field and wind-tunnel data. We propose a picture of canopy turbulence in which eddies associated with inflectional instabilities are modulated by larger-scale, inactive turbulence, which is quasi-horizontal on the scale of the canopy.     

A wind tunnel study of turbulent flow around single and multiple windbreaks, part I: Velocity fields

This paper describes wind-tunnel experiments on the flow around single and multiple porous windbreaks (height H), sheltering a model plant canopy (height H/3). The mean wind is normal to the windbreaks, which span the width of the wind tunnel. The incident turbulent flow simulates the adiabatic atmospheric surface layer. Five configurations are examined: single breaks of three solidities (low, medium, high; solidity = 1 - porosity), and medium-solidity multiple breaks of streamwise spacing 12H and 6H. The experimental emphases are on the interactions of the windbreak flow with the underlying plant canopy; the effects of solidity; the differences in shelter between single and multiple windbreaks; and the scaling properties of the flow. Principal results are: (1) the "quiet zones" behind each windbreak are smaller in multiple than single arrays, because of the higher turbulence level in the very rough-wall internal boundary layer which develops over the multiple arrays. Nevertheless, the overall shelter effectiveness is higher for multiple arrays than single windbreaks because of the "nonlocal shelter" induced by the array as a whole. (2) The flow approaching the windbreak decelerates above the canopy but accelerates within the canopy, particularly when the windbreak solidity is high. (3) A strong mixing layer forms just downwind of the top of each windbreak, showing some of the turbulence and scaling properties of the classical mixing layer formed between uniform, coflowing streams. (4) No dramatic increase in turbulence levels in the canopy is evident at the point where the deepening mixing layer contacts the canopy (around x/H = 3) but the characteristic inflection in the canopy wind profile is eliminated at this point.     

Measurements of flow over an elongated ridge and its thermal stability dependence: The mean field

Measurements of mean wind flow and turbulence parameters have been made over Cooper's Ridge, a 115 m high elongated ridge with low surface roughness. This paper describes measurements of the streamwise and vertical variations in the mean field for a variety of atmospheric stability conditions. In near-neutral conditions, the normalised speedup over the ridge compares well with measurements from Askervein (Mickleet al., 1988). The near-neutral results are also compared to an analytical flow model based on that of Huntet al. (1988a). Measured streamwise variations show less deceleration at the foot of the hill and slightly more acceleration at the crest of the hill than does the model. In non-neutral conditions, the speedup over the ridge reduces slightly in unstable conditions and increases by up to a factor of two in stable conditions. The model is modified to allow boundary-layer stability to change the upwind wind profile and the depths of the inner and middle layers. Such a modification is shown to describe the observations of speedup well in unstable and weakly stable conditions but to overestimate the speedup in moderate to strongly stable conditions. This disagreement can be traced to the model's overestimation of the upstream scaling velocity at the height of the middle layer through its use of a stable wind profile form which has greater shear than that of the observed profiles, in possible combination with the three-dimensionality of the ridge which would allow enhanced flow around, rather than over, the feature in more stable conditions.     

Turbulence in waving wheat

Measurements of mean and fluctuating velocities, surface pressure and stalk waving have been made in a uniform wheat canopy. Features of the vertical profiles of mean turbulence quantities are discussed in the context of the resonant waving of wheat stalks. The discrete and prominent peaks in the velocity spectra measured in and above the canopy are then analyzed in the light of the organized travelling wave-type structure or ‘honami’, observed in such crops on windy days. Prominent peaks in the spectra are identified with the arrival of gusts, the stalk-waving frequency, and the frequency of oscillations in canopy height. Two possible mechanisms are proposed to account for the observed height dependence of the peak frequencies, directly associated with stalk waving.     

Turbulent flow over a very rough,random surface

A knowledge of the nature of turbulent flow over very rough surfaces is important for an understanding of the environment of crops, forests, and cities. For this reason, a wind-tunnel investigation was carried out on the variations in mean velocity, Reynolds shear-stress, and other turbulence quantities in a deep turbulent flow over a rough surface having a fair degree of randomness in the shapes, sizes, and positions of its elements.There was a layer close to the surface with considerable variations in both mean velocity and shear-stress, and the horizontal scale over which the mean velocity varied was much larger than the average distance between roughness elements. Above this layer, whose depth was of the order of the spacing between roughness elements, shear stress was constant with height, and the velocity profile had a logarithmic form. The usefulness of both mean profile and eddy-correlation methods for estimating fluxes above very rough terrain is discussed in the light of these findings.     

A simple mathematical model of airflow in waving plant canopies

A simple mathematical model is proposed, which combines the effects of mean wind speed, plant spacing and the drag coefficients of individual plants to calculate the fluctuating airflow within a waving crop canopy. The model is non-linear and is only amenable to analytical treatment when linearized; however, the full non-linear version can be solved on an analogue computer.The linear and non-linear results show unexpectedly good agreement, and the success of the linearization allows clear conclusions to be drawn about the relationship between the elasticity, geometry and mean wind speed through a stand of plants and the fluctuating components of airflow and stalk motion.Finally, the analytical results are in qualitative agreement with wind-tunnel results from two model canopies with different characteristics.     

Modelling waving crops in a wind tunnel

Analysis of movie films of a field of barley, combined with observations of the motions of individual plants, show that single stalks oscillate at a well-defined natural frequency even when stimulated by turbulent winds. Treating single stalks as resonant cantilevers allows the use of standard engineering methods to determine their elastic properties. Armed with these values, the application of similarity analysis to the equation of motion of a single stalk leads to criteria for aeroelastic modelling of wheat plants in the wind tunnel. A representative value for the spacing of stalks in a small section of model wheat field was calculated by referring to published data on momentum absorption in a variety of real and model canopies. Preliminary measurements of first and second moments of velocity in the model appear to confirm the importance of including elastic properties in wind-tunnel simulations of airflow in flexible crops.     

A Re-Evaluation of Long-Term Flux Measurement Techniques Part II: Coordinate Systems

To convert measurements of windspeed, eddy flux and scalar concentration into estimates of surface scalar exchange, we implicitly or explicitly assimilate the measurements into mathematical statements of the mass balance in a control volume on a representative patch of the surface. The form of this statement depends on the coordinate system in which it is written and the coordinate system should be chosen so that measurements can be used optimally. This requirement imposes a set of conditions on the coordinates. Here we perform a comparative analysis of some candidate coordinate systems, concentrating on the Cartesian and physical streamline systems. We show that over gentle topography there are definite advantages in working in streamline coordinates. Transforming measurements of vector and tensor quantities measured in the reference frame, s _i, of the anemometer into the reference frame, e _i, of the chosen coordinate system involves using the measured statistics of the wind field to define three Euler rotation angles. We compare the method in most common use, which employs the components of the mean wind vector and the Reynolds stress tensor to define these angles, with the more recent planar-fit method that uses instead an ensemble of mean wind vectors to define the rotations. We find that, in real flows, the standard method has a previously unrecognized closure problem that ensures that the third rotation angle defined using the stress tensor or scalar flux vector will always be in error and often give unphysical results. An alternative procedure is recommended. Finally, the relationships between measurements and model outputs are discussed.     

Aerodynamic loads on a typical tension leg platform

The wind load effects on tension leg platforms have been recognized to be a significant environmental loading. An accurate assessment of the aerodynamic loads is, therefore, a prerequisite for the design of an economic and a reliable structure. The design codes and specifications recommend the use of a projected area approach that is thought to be conservative. The code recommendations fail to quantify aerodynamically induced forces in directions different to the mean wind flow. The interference and shielding effects suggested in some specifications provide only a simplistic view. Physical modeling as reported in this paper, therefore, continues to serve as the most accurate and practical means of predicting aerodynamic loads.The mean aerodynamic force and moment coefficients of a typical tension leg platform for various approach wind directions were measured on a scale model exposed to simulated flow conditions in a boundary layer wind tunnel. Major components on the upper deck of the model were designed for easy removal so that measurements could be obtained for different platform configurations. A parametric study was conducted to determine shielding and interference effects, i.e. the manner in which aerodynamic coefficients are influenced by the location and orientation of the ancillary structures on the platform, e.g. living quarters, flare boom, derricks, etc. The present paper addresses the wind tunnel modeling procedures and automated data acquisition and reduction methods. The aerodynamic force and moment coefficients with respect to the body and flow axes were reduced from the experimental measurements for azimuth angles of 0 to 360 degrees at 15-degree intervals. A total of eight configurations were monitored ranging from a platform configuration that included all the ancillary structures to the case where every deck component was removed. The aerodynamic coefficients obtained from the classification society recommended procedures provided conservative estimates in comparison with the measured values for all configurations. The results also illustrate that the interference effects among various ancillary structures on the platform are significant.